In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes eq...In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.展开更多
Regression-based decomposition of inter-industry earnings differentials shows that in 1988, 1995 and 2002, inter-industry earnings differentials made an increasing contribution to urban earnings inequality in China. T...Regression-based decomposition of inter-industry earnings differentials shows that in 1988, 1995 and 2002, inter-industry earnings differentials made an increasing contribution to urban earnings inequality in China. The primary reason for the widening gap lay in monopoly industries. At the same time, geographical location, educational level, type of enterprise ownership, type of occupation and whether the individual had a second job also contributed to rising earnings inequality, while age and being fully employed made a decreasing contribution. Therefore, if China is to reduce the earnings gap it is imperative that we remove barriers to labor market entry and break down some monopoly industries in the product market. Additionally, reducing obstacles to the free movement of labor and improving workers＇ educational level should also be important elements of the government＇s strategy for reducing the urban income gap in future.展开更多
Sparse subspace clustering(SSC),a seminal clustering method,has demonstrated remarkable performance by effectively solving the data sparsity problem.However,it is not without its limitations.Key among these is the dif...Sparse subspace clustering(SSC),a seminal clustering method,has demonstrated remarkable performance by effectively solving the data sparsity problem.However,it is not without its limitations.Key among these is the difficulty of incremental learning with the original SSC,accompanied by a computationally demanding recalculation process that constrains its scalability to large datasets.Moreover,the conventional SSC framework considers dictionary construction,affinity matrix learning and clustering as separate stages,potentially leading to suboptimal dictionaries and affinity matrices for clustering.To address these challenges,we present a novel clustering approach,called SSCNet,which leverages differentiable programming.Specifically,we redefine and generalize the optimization procedure of the linearized alternating direction method of multipliers(ADMM),framing it as a multi-block deep neural network,where each block corresponds to a linearized ADMM iteration step.This reformulation is used to address the SSC problem.We then use a shallow spectral embedding network as an unambiguous and differentiable module to approximate the eigenvalue decomposition.Finally,we incorporate a self-supervised structure to mitigate the non-differentiability inherent in k-means to achieve the final clustering results.In essence,we assign unique objectives to different modules and jointly optimize all module parameters using stochastic gradient descent.Due to the high efficiency of the optimization process,SSCNet can be easily applied to large-scale datasets.Experimental evaluations on several benchmarks confirm that our method outperforms traditional state-of-the-art approaches.展开更多
文摘In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.
文摘Regression-based decomposition of inter-industry earnings differentials shows that in 1988, 1995 and 2002, inter-industry earnings differentials made an increasing contribution to urban earnings inequality in China. The primary reason for the widening gap lay in monopoly industries. At the same time, geographical location, educational level, type of enterprise ownership, type of occupation and whether the individual had a second job also contributed to rising earnings inequality, while age and being fully employed made a decreasing contribution. Therefore, if China is to reduce the earnings gap it is imperative that we remove barriers to labor market entry and break down some monopoly industries in the product market. Additionally, reducing obstacles to the free movement of labor and improving workers＇ educational level should also be important elements of the government＇s strategy for reducing the urban income gap in future.
基金supported by the National Natural Science Foundation of China(No.62276004)the major key project of Pengcheng Laboratory,China(No.PCL2021A12)and Qualcomm.
文摘Sparse subspace clustering(SSC),a seminal clustering method,has demonstrated remarkable performance by effectively solving the data sparsity problem.However,it is not without its limitations.Key among these is the difficulty of incremental learning with the original SSC,accompanied by a computationally demanding recalculation process that constrains its scalability to large datasets.Moreover,the conventional SSC framework considers dictionary construction,affinity matrix learning and clustering as separate stages,potentially leading to suboptimal dictionaries and affinity matrices for clustering.To address these challenges,we present a novel clustering approach,called SSCNet,which leverages differentiable programming.Specifically,we redefine and generalize the optimization procedure of the linearized alternating direction method of multipliers(ADMM),framing it as a multi-block deep neural network,where each block corresponds to a linearized ADMM iteration step.This reformulation is used to address the SSC problem.We then use a shallow spectral embedding network as an unambiguous and differentiable module to approximate the eigenvalue decomposition.Finally,we incorporate a self-supervised structure to mitigate the non-differentiability inherent in k-means to achieve the final clustering results.In essence,we assign unique objectives to different modules and jointly optimize all module parameters using stochastic gradient descent.Due to the high efficiency of the optimization process,SSCNet can be easily applied to large-scale datasets.Experimental evaluations on several benchmarks confirm that our method outperforms traditional state-of-the-art approaches.
